so if I go and see there IP through site like whatismyip.com , it comes out to be same for both.

However if I try to connect through the IP that comes in ipconfig which are different for both of them, ServerSocket does not get connection from client.
That means they seem to be not connected that way.

Not knowing anything about your networking setup, I'd just assume you're going through cable/DSL/fiber so all the outside world would see is that IP address. That's not a reasonable way to find out IP addresses--check on each machine.

For example, I'm on a MBP and currently connected to another laptop (on same wireless network), another Mac (it's wired and sharing iTunes) and a Linux box (wired).

Your issue is (most likely) not due to *how* your machines are connected to your network.